By E. J. BUCHANAN Introduction
A thorough investigation of all equipment in a sugar factory covered by this title would result in a monumental publication. This relatively modest paper purports to draw attention to a few specific aspects of economy in juice heating. Considering the abundance of comprehensive articles on liquid-vapour and liquid- liquid heat exchangers appearing in chemical engineer- ing journals it is surprising that the superficial treatment of this subject as shown by articles in sugar journals indicates that little application is made of this valuable fund of knowledge in the sugar industry.
Although the empirical approach may be adequate for routine specification and control, the application of general chemical engineering techniques developed
in this field would facilitate the attainment of a maximum operating economy and the optimum design of new equipment. It is hoped that this article will produce a stimulus to the application of establish- ed heat engineering techniques to the economic design and operation of juice heaters and heat exchange equipment in general in the sugar industry.
Derivation of Heat Transfer Coefficients In the general case of heating juice flowing inside a tube we are concerned with convectional heat transfer to a liquid under turbulent flow. Consider for example a juice velocity of only 3 ft. per sec. through a 1.5 in.
i.d. tube. If the density is 65 lb per cu ft and the viscosity 0.5 cP, i.e. 0 . 5 x 6 . 7 2 x 10- 4=3.36x 10-4
90 Proceedings of The South African Sugar Technologists' Association — March 1966
lb/(ft)(sec), (taking conservative figures), then the value of the Reynolds number is:
NRe = Duρ/μ = (1.5x3x65)/(12x3.36xl0- 4)
= 7.25 x104
which is well over the laminar flow region (below a value of 2,100).
The overall heat transfer coefficient may be predict- ed from a knowledge of the physical conditions exist- ing on either side of the tube wall but since it is dependent on a number of variables it is usual to estimate individual coefficients for the inner and outer pipe surfaces and to summate these, as discussed later.
Liquid Film Coefficient Inside Tubes
The fluid adjacent to the pipe wall is in laminar flow, hence heat transfer through this film is by conduction and the liquid film resistance will be dependent on the Reynolds number, as well as the thermal conductivity and specific heat of the fluid, i.e.
hi = f(D,G,μ,k,c)
By dimensional analysis it may be shown that hiDik=f(DG/μ,cμk)
the three dimensionless groups being known respec- tively as, the Nusselt number (NN u), the Reynolds number (NR e) and the Prandtl number (NPr), i.e.
NNu = f(NRe,NPr)
A considerable amount of research has resulted in the correlation
hiD.k = 0.023(DG/μ)0.80(cμ/k)1/3
which holds for Reynolds numbers between 10,000 and 400,000 and Prandtl numbers between 0.7 and
12018. For liquids, this equation may be condensed to hi = 0.023G0 . 8k2 / 3c1 / 3,D0 . 2μ0 . 4 7 . . . (1) Equation (1) may be solved approximately by the use of the nomograph 3 in fig. 1.
Since μ decreases rapidly with an increase in temperature, the film coefficient increases and it is usual to calculate a mean coefficient for conditions prevailing at the mean temperature of the liquid in the exchanger. This is satisfactory for the case of low viscosity liquids where a small temperature difference prevails across the tube. However, in general it is necessary to estimate the actual wall temperature in contact with the heated fluid as discussed later.
Equation (1) shows that the liquid velocity is the most important factor determining the film coefficient inside the tubes. For example, if the liquid velocity was increased from 3 to 6 ft per sec (all other variables being constant) the film coefficient would increase, according to equation (1), by a factor of 1 .74. Con
sequently, the liquid velocity should be as high as possible, the upper limit being economically depen
dent on the incremental cost of the exchanger and the pumping charges.17
Outside Film coefficients
In the sugar industry we are concerned with the condensation of the low pressure steam in the case of
which apply for NRe in the film of less than 2,100. In practice these equations are conservative by about 20 per cent due to the effect of ripple on the film.
Dropwise condensation would give higher values, but in general it is safest to assume film-type con
densation for design purposes. When clean steam condenses on clean surfaces film-type condensation is always obtained.15 The investigations of Osment et al. 2 0have shown that overall heat transfer coeffici
ents in surface condensers may be doubled by the injection of filming amines into the steam space to promote drop-type condensation.
It is interesting to note from equations (2) and (3) that the relative effectiveness of steam condensation rates for horizontal and vertical tubes is
Assuming that the tubes are 1.6 in outside diameter, 12 ft. long and 8 tubes are arranged in the average vertical stack, equation (4) indicates that the hori
zontal heater will have a 70 per cent greater conden
sing film coefficient than the vertical heater.
The factor N in equation (2) accounts for the effect of the accumulating condensate film around a vertical stack of horizontal tubes, the film coefficient diminish
ing for lower tubes. For this reason a staggered arrangement of the tubes would promote a higher film coefficient.'1
Film and Wall Temperatures
In the case of turbulent liquid flow through tubes, the difference in temperature between the bulk of the liquid and the film in contact with the tube wall is often neglected particularly if the temperature difference across the wall is small. However, if correction is necessary then equation (1) is multiplied by
viscosity being the only variable which is significantly effected by temperature.
juice heaters and also in the transfer of heat through liquid films outside tubes in liquid-liquid heat ex
changers. In the latter case, equation (1) may be used by substituting De for D;
De = 4% free area of cross section/perimeter which applies when the flow is parallel to the tubes and fully turbulent, i.e. NR e> 10.00021.
For steam-heated tubes, the installation may be either horizontal or vertical. For film condensation, Nusselt has developed the following equations 19
Proceedings of The South African Sugar Technologists' Association — March 1966 91
Estimation of the wall temperature may be achieved by a trial-and-error method using the equation18
scale, the inside film, tube wall, outside film and outside scale as shown by equations (8) and (9). The overall coefficient may be based arbitrarily on either the inside or outside tube area but the chosen area should be stated. The outside area is the most usual choice.
In the above equations the diameter ratios correct the values of the individual coefficients to the selected area. In some cases one film coefficient may be considerably greater than any of the others so that the diameter conection has a small effect. In this case it is convenient to abbreviate the equation eliminating the diameters and to express the overall coefficient in terms of the tube-side area in contact with the highest resistance, i.e. lowest film coefficient.18
The coefficients hdi and hdo represent the fouling factors for the inner and outer tube surfaces, respec- tively. Their combined values may be determined by comparing the overall coefficients of the clean and scaled heaters. If however the outer wall is clean, the inside fouling factor may be calculated 14 fiom
Another method of determining the fouling factor is by means of a Wilson plot, 1, 15 in which the reciprocal of U is plotted as a function of u0.8 for both clean and fouled surfaces.
Estimation of Coefficients in Practice
There is little information available on heat transfer coefficients of juice heaters under factory conditions in South Africa. For this reason, even fundamental questions such as the choice between vertical and horizontal heaters or the optimum juice velocity are often still a matter of controversy even after several decades of experience. In spite of this lack of practical information, many of the problems may be clarified by applying the standard chemical engineering techniques outlined in the previous section.
The author has determined Uo on several local heaters and found rather low values of not more than
180 after being cleaned inside the tubes. One of these heaters will be used as an example of the application of the methods developed previously.
Example
The heater chosen for analysis is a horizontal tubular type with tubes arranged in a series of vertical in which, h,- is estimated from equation (1) and h0 from
equation (2) or (3). For the preliminary estimation of h„ the outer wall temperature is chosen midway between the bulk temperatures on either side of the wall.
The wall temperature is then obtained from
In the case of condensing a vapour outside a tube, the condensate is normally under viscous flow and the temperature drop across the film is more significant.
The mean film temperature is evaluated from 19 The wall temperature is assumed initially and the value of the film coefficient, calculated by equation (2) or (3), is checked using equation (6).
For approximate working figures equation (1) is used without correction and the steam film coefficient may be determined from nomographs such as fig.
2 25
Overall Heat Transfer Coefficients
The overall heat transfer coefficient is compounded from the individual resistances due to the inside
92 Proceedings of The South African Sugar Technologists" Association —• March 1966
Tube wall transfer rate:
The tube wall coefficient may be determined as inferred from equation (8). Assuming 70-30 brass tubes:
km = 60 Btu(hr)(sqft)(°F/ft)
xw = (1.625-1.495) 12 = 0.108 sq ft km/xw. = 5,556 Btu (hr)(sq ft)(oF)
Steam side film coefficient:
Generally it is preferable to use nomographs based on practical figures rather than the method discussed previously, the limitations of which have been pointed out. The nomograph by Stoever25 fig. 2 may be applied for an initial estimate.
The condensing temperature is 218° F and λ = 966 Btu/lb
q = 112 x 2,000 v 0.92(192-96)
= 1.978 x 107 Btu/hr
Go = 1.978 107/(966 x 2,010)
=: 10.19 lb/(sq ft)(hr) ND' o = 16 x 1.625 = 26
From fig. 2 (see dotted line example), the correction factor is 0.34. Assuming a wall temperature of (218 +
144)/2 = 181oF the mean condensate film temperature is, from equation (7)
tf = 218-3(218-181 )/4 = 190o F
and the corresponding base factor may be calculated from
Fb = 11.2tf + 1,320 (see fig. 2)
= 11.2 190 + 1,320
= 3,460
The film coefficient is calculated from K = Fb x Fc (see fig. 2)
= 3,460 x 0.34
= 1,180 Btu/(sq ft)(hr)(oF)
Check on Wall Temperature:
From equation (6) stacks, 18 per stack on the average. The following data
apply:
Brix of juice = 14.7°
Juice rate = 1 1 2 ton,hr
Heating range = 96° F to 192° F Vapour satn. temp. = 218° F Effective tube length = 11 ft 10? in Inside tube diameter = 1.495 in Outside tube diameter = 1.625 in
Total heating surface = 2,010 sq ft (based on o.d.) Tube arrangement -- square pitch, average 16 per
stack
Tubes per pass --- 18
Heat Transfer Coefficient—Clean Tubes Inner Film Coefficient:
It may be assumed that flow is turbulent (as calcu
lated earlier) hence the inner film coefficient may be estimated from equation (1). The mean juice temper
ature is
(96 + 192)/2 = 144° F or 62° C
Using the physical data in the appendix as an approximation:
μ = 0.65 x 2.42 lb (ft)(hr) k = 0.346 Btu (ft)(hr)(°F) c = 0.92 Btu/(lb)(°F) Di = 1.495/12 = 0.125 ft
Inside section = 3.1416 x (0.125)-4 - 0.0123 sq ft tube
G = 112 x 2,000/(18 x 0.0123)
= 1.012 106 lb(sqft)(hr) From equation (1)
which is sufficiently close to the value assumed above.
Corrected inside coefficient:
Using equation (5) h, may be corrected to the wall temperature at which μw = 0.45 cP and hence
hi = 860 (0.65/0.45)0.14 = 906
This value is obtained approximately, following the example (dotted line) in fig. 1.
Checking again with equation (6)
Proceedings of The South African Sugar Technologists'' Association — March 1966 93
Measurement of U„ in practice for this particular heater under the given operating conditions provided the value of Uod = 157.
Little information is available on fouling factors in cane juice heaters. The Sugar Research Institute,
Mackay, 2 have conducted investigations on a pilot scale heater which, upon analysis, provided results in close agreement with U0 = 450 for a clean heater under the present conditions. The thermal conduc- tivity of the scale was calculated as about 0.3 and after 100 hours operation the thickness of scale was about 0.006 inches.
Applying this information, it is possible to estimate approximately the effects of fouling. Assuming for example that the average scale thickness between cleanings was 0.005 inches, then the fouling factor would be
hdi = k/x (0.3/0.005)12 = 720 and from equation (10)
This assumes no outside fouling. The Sugar Re- search Institute, Mackay,2 observed on their pilot heater that the overall heat transfer coefficient decreased by as much as 30 per cent during a season due to fouling outside the tubes. The pilot heater was operated on factory exhaust steam. The heater examin- ed in the present paper had been operating for a complete season, hence a similar degree of fouling could be expected. In the absence of any confirmatory data, if this is applied to the present case
This value for hdo is quite feasible even for a very thin film. Oil, for example, has a thermal conductivity as low as 0.07 so that a fouling factor of 671 could be accounted for by an oil film of thickness
In this connection it should be pointed out that the dropwise condensation promotion due to common oils is relatively inefficient (c.f. filming amines) and of short duration, particularly when other fouling com- pounds are present.20
The various heat transfer coefficients and fouling factors for the heater in question are summarised in Table 1.
Vertical vs. Horizontal Heaters
Equation (4) indicates that, all other conditions being equal, the film coefficient for condensation in a horizontal heater will be greater than for a vertical heater provided that
Most tubes in cane juice heaters have Do = 1.625/ 12 ft and L = 12 ft so that equation (11) would read
Proceedings of The South African Sugar Technologists' Association — March 1966
Hence the condensing film coefficient for a horizontal heater is always greater than for a vertical heater. For the heater discussed above for example, N = 16 and from equation (4)
hoh/hov = 1 .486 or hov/hoh = 0.672 The condensing film, coefficient (Table I) for a similar vertical heater would have been
hov = 1,180 X 0.672 = 793
and the overall coefficient would have been (Table I)
Thus 28 per cent more heating surface would be required for a clean vertical heater than for a clean horizontal heater with N = 8. The working value may range between 13 and 28 per cent, averaging about 20 per cent.
The existence of this difference between horizontal and vertical heaters cannot be disputed since it is based on calculations which have been substantiated by a large number of practical results from a wide field of application. Considering that overall coeffici- ents are dependent on so many variables such as steam and juice properties, juice velocities, degree of inside and outside fouling, etc., it is not difficult to imagine why some sugar factory designers are un- willing to accept that this difference exists in practice.
A survey of costs per sq ft of heating surface for juice heaters from local suppliers has indicated that vertical heaters are normally about 5 per cent higher than horizontal heaters. This means that the total initial cost is 20 + 5 = 25 per cent higher for vertical heaters.
The average price of heaters is R6 per sq ft and for a 250 tch factory, with heating surface at 45 sq ft per tch,11 the additional initial cost for correctly specified vertical heaters would be
To this must be added an additional 20 per cent on Tunning costs.
This cost difference should be viewed in the light of convenience of installation and operation for the particular factory design. The choice of a vertical heater on either of these grounds is not necessarily based on economy and consequently falls beyond the scope of this paper.
Economical Waste Heat Recovery
A typical example of the recovery of waste heat in a sugar factory is the preheating of cane juice by means of evaporator vapours and condensates. A number of useful calculations has been presented by
F I G U R E 3. Nomograph f o r the evaluation of equations (13) and (14) in the economic optimization cf waste heat recovery exchangers.26 Copyright 1944 by the American Chemical Society and reprinted by permission of t h e copyright o w n e r .
and 13 per cent more heating surface would be re- quired for a vertical heater. If, in addition, the heating surfaces were clean then
which would require an increase of 9 per cent in heating surface. This is a very conservative example since the exchanger was poorly designed (square pitch) and heavily scaled. Had the tubes been staggered,16
the number in a vertical row might have been reduced to eight. Using fig. 2, N = 8 hence NDo = 13, Fc = 0.42 and Fb = 3,460. Hence hoh = 0.42 x 3, 460 = 1453. The overall film coefficient would have been
94
Economy by Control
Since convection currents cause entrainment in clarifiers it is essential that the temperature of entering juice be stable. In the absence of proper control this
is often achieved by superheating and flashing to constant temperature. The heat from flashed vapour is rarely recovered in spite of the fact that (e.g.) a 250 tch factory by maintaining 10° F of superheat in the juice would (if coal was being burnt) lose R7,200 per year in heat.*
Although the maintenance of 10° F is only necessary under conditions of very poor control there are cases where, due to excessive fluctuation in juice velocities and steam pressures even 10° F flash is insufficient to maintain a safe margin for occasional peak flow rates and resulting temperature drops below boiling.
In such extreme cases automatic temperature control is not only a labour saving device but could be viewed as an economic advantage.
It should be mentioned that the maintenance of a small amount of flash is usually regarded as essential for the release of air from the juice and the acceleration of otherwise slow reactions but this discussion refers to excessive flash.
Modes of Control
Conventional Control: The normal method of control is to measure the outlet juice temperature and adjust the steam control valve to maintain the desired temperature. This usually requires a wide proportional band setting to maintain stability and hence reset response to correct the resulting offset due to load changes. When rapid changes in throughput occur the resulting short-term error can be corrected in part by the addition of derivative response.
Condensate Throttling: By throttling the condensate, a less responsive control action will be achieved but this system has the advantage of reduced initial cost.
The behaviour of this type of system is difficult to predict.22 It also assumes an oversized heating surface and is prone to the danger of excessive fouling on the steam side of the tubes if condensates are contaminated with oil, etc.
Pressure-Cascade Control: The most rapid recovery to load disturbances may be attained by cascading the output of a standard three-mode temperature controller into the set point of a proportional plus reset pressure controller. Changes in steam pressure are corrected directly by the pressure controller. Load changes are sensed rapidly by a change in shell pressure which is compensated by the pressure controller. The temperature control system senses the residual error and resets the pressure controller set point.
Minimum Temperature Control: In cases where more elaborate control is excluded due to cost, sharp downward peaks in the flashed juice temperature recording chart may be eliminated by the injection of
* The above amount was calculated assuming 4,600 hr/yr 12000 Btu/lb coal, a boiler efficiency of 70%, 20% recycle of filtrate on juice and 0.242c/lb coal.
Proceedings of The South African Sugar Technologists' Association - March 1966 95
Happel7 for determining the economic optimum heat recovery and these are discussed below.
Recovery of Heat from Vapour or Exhaust Steam For the recovery of heat from steam or vapour at a constant temperature, th to a liquid which is heated without vaporization from temperature tc1 to tc2
(th - tc2) opt. = H/H, . . . (12) where H = 114rE/UY
This calculation assumes a knowledge of the total exchanger costs and marginal cost of steam production.
The optimum value of tc2 may then be determined.
This equation applies also to the case of waste heat recovery from flue gases, as in a waste heat boiler, where the heated liquid temperature remains constant and the recovered heat is utilised in steam production.
Recovery in Countercurrent Liquid-Liquid Exchangers For the recovery of heat from a hot liquid at temperature th1 to a cooler liquid at temperature tc1
in a counlereurrenl (1-1) exchanger, the optimum final temperature th2 of the hot liquid may be deter- mined from
. . . (13)
For any given problem the right hand side of the equation will be a constant and R will be fixed.
Recovery in Multipass Exchangers
Pre-heating of juice by condensates is commonly carried out in multipass exchangers of the 1-2 or 2-4 type as described by Webre.27 For the case of a 1-2 type exchanger, the following equation applies in a similar manner to the previous expression
. . (14) For exchangers of the 2-4 type graphical differenti- ation is most convenient for the evaluation of P.
Ten Broeck26 has presented a convenient nomo- graph for the evaluation of P for all three types of liquid-liquid exchangers. This nomograph is re- produced in fig. 3. The evaluation, of Ht, the incre- mental cost of supplying heat, may present compli- cations it is composed, of several elements. First there will be a saving resulting from decreased fuel consumption. The value of the heat saved may be determined from the price of fuel, its heating value and the expected furnace efficiency. The cost of supplying heal, by a furnace will include the fixed charges on incremental cost of furnace as well as the fuel cost. Also the recovery of waste heat may reduce condensing and cooling costs.